Geodesic
The Complete (Lp , Lp ) Mapping Properties of Some Oscillatory Integrals in Several Dimensions
Canadian journal of mathematics, Tome 53 (2001) no. 5, pp. 1031-1056

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that the operators $\int{_{\mathbb{R}_{+}^{2}}{{e}^{i{{x}^{a}}\cdot {{y}^{b}}}}\varphi (x,y)f(y)dy}$ map ${{L}^{p}}({{\mathbb{R}}^{2}})$ into itself for $p\,\in \,J\,=\,\,\left[ \frac{{{a}_{1}}+{{b}_{1}}}{{{a}_{1}}+(\frac{{{b}_{1}}r}{2})},\frac{{{a}_{1}}+{{b}_{1}}}{{{a}_{1}}+(1-\frac{r}{2})} \right]$ if ${{a}_{l}},{{b}_{l}}\ge 1$ and $\varphi (x,y)=|x-y{{|}^{-r}},0\le r<2$ , the result is sharp. Generalizations to dimensions $d\,>\,2$ are indicated.
DOI : 10.4153/CJM-2001-040-9
Mots-clés : 42B20, 46B70, 47G10 
Sampson, G.; Szeptycki, P. The Complete (Lp , Lp ) Mapping Properties of Some Oscillatory Integrals in Several Dimensions. Canadian journal of mathematics, Tome 53 (2001) no. 5, pp. 1031-1056. doi: 10.4153/CJM-2001-040-9
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